Block #213,986

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/17/2013, 4:57:38 AM · Difficulty 9.9227 · 6,578,709 confirmations

2CC

Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header

Block Hash

ac21b203fd01e5c9a3297c069b525953dc1df6237a44efaaff5cc000477e2f09

View on Chainz ↗

Height

#213,986

Difficulty

9.922729

Transactions

Size

5.03 KB

Version

Bits

09ec37f0

Nonce

1,164,794,089

Timestamp

10/17/2013, 4:57:38 AM

Confirmations

6,578,709

Merkle Root

0d56b225f125a88be3d077ed8d9fb43fdd3b47b18a6b2bf80b8ad12f8403e8df

Transactions (1)

Coinbase0d56b225f125a8…8ad12f8403e8df

1 in → 147 out10.0800 XPM4.94 KB

ATWZA6yR…2S7RB9ab AHqZtsfn…WrCGjM3J ASBFyn8Q…gDcPEt7u AZfENRFB…e1WGhmHp AdDjcFF6…qGKzhryp

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

9.117 × 10⁹²(93-digit number)

91175503444604069759…35766458994327219201

Discovered Prime Numbers

p_k = 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

origin + 1

9.117 × 10⁹²(93-digit number)

91175503444604069759…35766458994327219201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.823 × 10⁹³(94-digit number)

18235100688920813951…71532917988654438401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.647 × 10⁹³(94-digit number)

36470201377841627903…43065835977308876801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.294 × 10⁹³(94-digit number)

72940402755683255807…86131671954617753601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.458 × 10⁹⁴(95-digit number)

14588080551136651161…72263343909235507201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.917 × 10⁹⁴(95-digit number)

29176161102273302323…44526687818471014401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.835 × 10⁹⁴(95-digit number)

58352322204546604646…89053375636942028801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.167 × 10⁹⁵(96-digit number)

11670464440909320929…78106751273884057601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.334 × 10⁹⁵(96-digit number)

23340928881818641858…56213502547768115201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.668 × 10⁹⁵(96-digit number)

46681857763637283717…12427005095536230401

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer